Answer:
The first 12 terms of the series are represented by:
[tex]f(12) = \Sigma\limits_{i = 1}^{12} [(-1)^{n}\cdot 2^{n-1}] = -1 + 2 - 4 + 8 - 16 + 32 - 64 + 128 -256 + 512 - 1024 + 2048[/tex]
Step-by-step explanation:
The summation notation for the series [tex]-1 + 2 -4 + 8 -16...[/tex] is represented by the expression [tex]f(n) = \Sigma\limits_{i = 1}^{n} [(-1)^{n} \cdot 2^{n-1}][/tex].
The first 12 terms of the series are represented by:
[tex]f(12) = \Sigma\limits_{i = 1}^{12} [(-1)^{n}\cdot 2^{n-1}] = -1 + 2 - 4 + 8 - 16 + 32 - 64 + 128 -256 + 512 - 1024 + 2048[/tex]
jane bought 5 3/5 boxes of raspberries and 2 1/4 boxes of strawberries. How much more boxes of raspberries did jane buy?
Answer: 3 7/20
Step-by-step explanation:
5 3/5 - 2 1/4
Find GCD.
5 12/20 - 2 5/20
3 7/20 more boxes of raspberries than strawberries
Can someone higher please help ?
.....................................................................................
Answer: -0.833 (repeating decimal)
Step-by-step explanation: fg(x) means plug the g(x) equation into f(x), and for gf(x) it’s vice versa:
Fg(x) = 3x^2 - 1 + 2
Gf(x) = 3(x + 2)^2 - 1
First, we should simplify gf(x) to eliminate the (x + 2)^2:
3(x^2 + 4x + 4) - 1
3x^2 + 12x + 12 - 1
3x^2 + 12x + 11
Second, simplify fg(x) by solving -1 + 2: 1
Now, we can set the two equations equal to each other and solve:
3x^2 + 1 = 3x^2 + 12x + 11 (subtract 3x^2 from each other and 1 from 11)
-10 = 12x (Divide)
-0.8333... = x
To make sure this answer is correct, plug -0.833 into the original equations and set them equal to each other:
3(-0.833)^2 + 1 = 3(-0.833)^2 + 12(-0.833] + 11
3.083 = 3.083
Which is the equation of the given line?
Answer:
y = 1
Step-by-step explanation:
since its a horizantal line
if u take any 2 points and find the slope, for example if we take points (1, 1) and (4, 1) the slope will be 0/3 which is zero
y = 0x + b
so there is basically no x in this case
so y = b
now plug in a point from the line, (1, 1)
y = mx + b
y = 0x + b
1 = 0(1) + b
1 = 0 + b
1 = b
b = 1
final equation:
y = 0x + 1
y = 1The number of members in a labor union is 240, and the number increases by 5% each year. Find the number of members after 4 years.
Answer: 292
Step-by-step explanation:
Given
There are 240 members in a labor union
The number increases by 5% each year
After 1 year it is
[tex]\Rightarrow 240+5\%\times 240\\\Rightarrow 240(1+0.05)[/tex]
After 2 years
[tex]\Rightarrow 240(1+0.05)+5\%\times 240(1+0.05)\\\Rightarrow 240(1+0.05)(1+0.05)=240(1+0.05)^2[/tex]
Similarly, after 4 years
[tex]\Rightarrow 240(1+0.05)^4\\\Rightarrow 291.72\approx 292[/tex]
which table represents a linear function? HELP FAST PLEASE
Answer:
the bottom left
Step-by-step explanation:
A linear function will have a constant slope so the bottom left graph is the only one with a constant slope. The y-values are all increasing by 2.
Can someone solve these for me?
Answer:
In order of pictures,
Picture #1: 230
Picture #2: 140
Picture #3: 9.9
Picture #4: 13.5
Picture #5: 7.07
Step-by-step explanation:
I am not entirely sure that 3 - 5 are correct, but I know that 1 and 2 are correct. I am sorry if they are incorrect.
Hope that this helps!
What is the area of the shape
A local computer company had a big sale the day after Thanksgiving and sold 192 computers for $452 each. Which is a good estimate for the amount of money they made on those computers that day?
A) $900
B) $9,000
C) $90,000
D) $900,000
Answer:
90,000
Step-by-step explanation:
As an estimate
200 * 450
which is 90,000
What is the line segment from the center of the circle to any point on the circle
please help me Answer this question
Step-by-step explanation:
the circle to any point on the circle
Answer:
Radius
.....................
Simplify
1/6 / 1 3/8
Answer:
1/6 = 1/6 (already simplified) 1 3/8 = 11/8
Step-by-step explanation:
You can paint a room in 8 hours. Working together, you and a friend could paint the same room in just 5 hours. How long would it take your friend to paint the room alone.
Answer:
friend alone could do it in 13 hours and 1/3
Step-by-step explanation:
Your rate = room/8
friends rate = room/x
combined rate = room/8 + room/x
= room(x+8)/(8x)
then
5 = room / [room(x+8)/(8x)]
5 = 8x/(x+8)
8x = 5x + 40
3x = 40
x = 40/3 = 13 1/3
friend alone could do it in 13 hours and 1/3
PLEASE HELP ME ON THIS
Answer: C
Step-by-step explanation:
56,252 rounded to the nearst ten thousandths
Answer:
60,000
Step-by-step explanation:
Answer:
60,000
Step-by-step explanation:
Which of these tables represents a function?
Table A
Table B
Table C
Table D
ARE the square root of the positive integer irrational? if not given an example of the square root of a number that is a rational number
9514 1404 393
Answer:
no; √4 = 2
Step-by-step explanation:
If an integer is the square of another integer, its square root is rational. For example, 9 = 3², so √9 = 3, a rational number.
The square root of an integer is irrational if and only if the integer is not a perfect square.
9. If PQRS is a kite, find RQ. *
17 ft.
23 ft.
30 ft.
12 ft.
Answer:
17 ft
Step-by-step explanation:
The triangle on the bottom left is a right triangle.
a² + b² = c²
(8 ft)² + (15 ft)² = (RQ)²
64 ft² + 225 ft² = (RQ)²
(RQ)² = 289 ft²
RQ = 17 ft
vTo estimate the parameter stated in question 2, the following was done. A simple random sample of 22 students who attended a review session was selected, and the mean grade on test 7 for this sample of 22 students was 85 with a standard deviation of 9.8. An independent simple random sample of 47 students who did not attend a review session was selected, and the mean grade on test 7 was 77 with a standard deviation of 10.6. If appropriate, use this information to calculate and interpret a 90% confidence interval for the difference in the mean grade on test 7 for all students who attended a review session and for all students who did not attend a review session.
Answer:
The 90% confidence interval for the difference in the mean grade on test 7 for all students who attended a review session and for all students who did not attend a review session is (3.7, 12.3).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
A simple random sample of 22 students who attended a review session was selected, and the mean grade on test 7 for this sample of 22 students was 85 with a standard deviation of 9.8.
This means that:
[tex]\mu_A = 85, s_A = \frac{9.8}{\sqrt{22}} = 2.09[/tex]
An independent simple random sample of 47 students who did not attend a review session was selected, and the mean grade on test 7 was 77 with a standard deviation of 10.6.
This means that:
[tex]\mu_N = 77, s_N = \frac{10.6}{\sqrt{47}} = 1.55[/tex]
Distribution of the difference in the mean grade on test 7 for all students who attended a review session and for all students who did not attend a review session.
Mean:
[tex]\mu = \mu_A - \mu_N = 85 - 77 = 8[/tex]
Standard deviation:
[tex]s = \sqrt{s_A^2 + s_B^2} = \sqrt{2.09^2 + 1.55^2} = 2.6[/tex]
Confidence interval:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
Now, find the margin of error M as such
[tex]M = zs[/tex]
So
[tex]M = 1.645*2.6 = 4.3[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 8 - 4.3 = 3.7
The upper end of the interval is the sample mean added to M. So it is 8 + 4.3 = 12.3
The 90% confidence interval for the difference in the mean grade on test 7 for all students who attended a review session and for all students who did not attend a review session is (3.7, 12.3).
The odds of winning a rifle are 1:9 the probability of winning a carnival game is 0.15 does the raffle or the carnival game give you better chance of winning
Answer:
Hence the carnival game gives you better chance of winning.
Step-by-step explanation:
Let the event of win be given by 1/10 in the game of rifle then the event of loose is given by 9/10
the
Odds in favor of a game are given by = P(Event)/ 1- P(Event)
Odds in favor of winning a rifle are given by = 1/10/ 1- 1/10
=1/10/9/10
=1/9
= 0.111
The probability of winning aa rifle game is 0.111
The probability of winning the carnival game is 0.15
Comparing the two probabilities 0.111:0.15
The probability of winning carnival game is greater than winning a rifle game
0.15>0.11
Hence the carnival game gives you better chance of winning.
What is the end behavior of this radical? f(x) = 4 square root x - 6
Answer:
I think you can answer it with a chart, I guess, of course I'm not sure♀️
Simplify (-32) divided by (-4)
Answer:
[tex] \frac{8}{1} [/tex]
Step-by-step explanation:
[tex] \frac{ - 32}{ - 4} [/tex]
Reduce factor by 4
[tex] \frac{ - 8}{ - 1} [/tex]
A negative divided by a negative equal positve so
[tex] \frac{8}{1} [/tex]
the simplest form of 32/4 is 8/1
find the GCD ( or HCF) of numerator and denominator GCD of 32 4 is 4
divide both the numerator and denominator GCD
32/4 ÷ 4/4
reduce fraction: 8/1
therefore, 32/4 simplify to lowest terms is 8/1.
Work out the mean for the data set below: 5, 6 Give your answer as a decimal.
Answer:
5.5
Step-by-step explanation:
5 + 6 =
11 / 2 =
5.5
HEKLPP
AINL
WILL
GIVE BRAINLIST
Answer:
2option is the correct answer
An article reported that for a sample of 58 kitchens with gas cooking appliances monitored during a one-week period, the sample mean CO2 level (ppm) was 654.16, and the sample standard deviation was 164.55. (a) Calculate and interpret a 95% (two-sided) confidence interval for true average CO2 level in the population of all homes from which the sample was selected. (Round your answers to two decimal places.) 611.81 , 696.51 ppm
Answer:
95% Confidence Interval = (611.81 ppm, 696.51 ppm)
Step-by-step explanation:
The formula for Confidence Interval is given as:
Confidence Interval = Mean ± z × s /√n
Mean = the sample mean/average = 654.16
s = the sample standard deviation = 164.55
z = z score of 95% confidence interval = 1.96
Confidence Interval =
654.16 ± 1.96 × 164.55/√58
= 654.16 ± 42.348
Hence,
654.16 - 42.348
= 611.812
Approximately to two decimal places = 611.81 ppm
654.16 + 42.348
= 696.508
Approximately to two decimal places = 696.51 ppm
Therefore, the 95% (two-sided) confidence interval for true average CO2 level in the population of all homes from which the sample was selected is (611.81 ppm, 696.51 ppm).
What are some basic steps that you can take to protect yourself from identity theft or fraud?
1. Use sharpie to cover up private information before throwing it away (because people can look through your trash for your info). For example: credit card information, your address, etc.
2. Secure your mail box. Get a lock to make sure that people won't steal your credit card information.
3. Never ever leave your receipts behind.
4. Don't lose your credit card!! People can steal it can spend your money!
5. Just don't give random people or friends your credit card information...
Well, I hope this helped! Be careful and stay safe!
This dot plot is not symmetric, and the data set has two
extreme values.
.
2
3
8
What is the best measure of center for this dot plot?
O A. The mean absolute deviation (MAD)
B. The interquartile range (IQR)
C. The median
D. The mean
Answer:
C: The median
Step-by-step explanation:
A box contains 4 yellow markers, 3 blue markers, 6 black markers and 2 red markers. Suppose a marker is chosen randomly, and then returned to the box.
Determine the probability of selecting a yellow marker, then a red marker.
Answer:
4+3+6+2 = 15
Step-by-step explanation:
selecting a yellow marker 4/15
selecting a red marker 2/15
tam
If ABCD is dilated by a factor of 2, the
coordinate of A' would be:
5
4
3
С
2
B
1
-8 -7 -6
-5
-3-2
-10
1
2
3
5
6
7
8
9 10
А
-2
D
-3
A' = ([?], [D
Answer:
-6,-2 is the answer!!
Step-by-step explanation:
The coordinate of A' would be (-6, -2)
Dilation of figureDilation is a transformation technique that changes the size of an object by a scale factor "k"
From the diagram shown, the measure of the coordinate point is given as (-3, -1).
If the coordinate A is dilated by a factor of 2, the resulting coordinate A' will be given as:
A' = (2(-3), 2(-1)) = (-6, -2)
Hence the coordinate of A' would be (-6, -2)
Learn more on dilation here: https://brainly.com/question/3457976
if a line passing through (4,-p) and (-2,6)is parallel to 2y+3x= -3, find p.
Use the Law of Cosines to find the measure of ∠F. Round to the nearest degree.
f = 5, g = 6, h = 7
Use: f² = g² + h² – 2gh cos F
Answer:
Solution given.
f = 5, g = 6, h = 7
<F=?
we have;
f² = g² + h² – 2gh cos F
5²-6²-7²=-2×6×7 cos F
-60/-84=cos F
F=cos-¹(5/7)=44.41°
<F=44.4° is a required answer
Please help fasst???!!! Plzzzx
Answer:
y = 10(½)^(x)
Step-by-step explanation:
In writing exponential functions passing through points, we will just substitute the x and y values in each case into y = ab^(x).
Now, for point (-1, 20), the exponential function is; 20 = ab^(-1)
20 = a/b
For the point (1, 5), the exponential function is; 5 = ab^(1)
5 = ab
From 20 = a/b, we have; a = 20b
Thus, putting 20b for a in 5 = ab, we have;
5 = 20b(b)
b² = 5/20
b² = 1/4
b = √(1/4)
b = 1/2
Since a = 20b, then;
a = 20 × 1/2
a = 10
Thus, from y = ab^(x), we have;
y = 10(½)^(x)